Recent content by logic smogic

So (a) is one since they will all be in the same state. But (c) will be E_{0} has degeneracy 2, since they will each be in the ground state, but each can either be up or down (or since the Hamiltonian is just a superposition of the different individual particles Hamiltonians, is it (3!=6)?)...

Any thoughts on this? The basic question here is: How does parity create selection rules? Perhaps someone could just lay out it for me, or point me to a nice tutorial. My book doesn't provide an example or anything of that sort, and I have an exam today! Thanks much.

a.) Oh, I think I see. I was thinking of degeneracy wrong? It refers to the number of possible states with a particular energy, not the number of particles occupying a specific energy level, right? How would I go about determining the degeneracy of a system like this? (of course, I'll do the...

[SOLVED] Identical Particles in a 1-D Harmonic Oscillator Homework Statement Three particles are confined in a 1-D harmonic oscillator potential. Determine the energy and the degeneracy of the ground state for the following three cases. (a) The particles are identical bosons (say, spin 0)...

[SOLVED] Perturbed Ground State Wavefunction with Parity Homework Statement A particle is in a Coulomb potential H_{0}=\frac{|p|^{2}}{2m} - \frac{e^{2}}{|r|} When a perturbation V (which does not involve spin) is added, the ground state of H_{0} + V may be written |\Psi_{0}\rangle =...

Because we're evalutating the system in equilibrium, right? Well, I'm saying that the total potential energy contribution from the springs is, V_{springs} = \frac{1}{2} k (y_{1} - y_{01})^{2} + \frac{1}{2} k [(y_{2}-y_{02})-(y_{1}-y_{01})]^{2} ...where you can see I've accommodated...

Homework Statement Find the total potential energy described by a system consisting of a mass hanging by a spring, connected to a second mass also hanging by a spring. Assume that the masses are the same, and the springs are identical (in spring constant and length). Homework Equations...

Ah, I must've had my convention backwards. That fixes everything - thanks!

Great, I got it. Thanks. Quick question, though. What is: \int_{0}^{2 \pi} \sin \phi d \phi Isn't it zero? But then all of my matrix elements would go to zero when evaluated in spherical coordinates (where \phi is evaluate from 0 \rightarrow 2 \pi). It seems like cheating to evaluate it...

I started in spherical, and had a tough time with it. But maybe I was turning to the definite integral tables too early. Looks like if I do integration by parts two (or maybe three?) times, it should take a familiar form. Alright, I'll give it a shot.

1. Problem Evaluate \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} z^{2} e^{-A \sqrt{x^{2}+y^{2}+z^{2}}} dxdydz 2. Useful Formulae none 3. Attempt at Solution Well, this is part of a much larger problem. I am trying to compute the dipole moment matrix elements...

Alright, it took 5 more pages of algebra, but I got it.

Progress Report Alright, I was clearly looking at this incorrectly. (Perhaps that's why I've had 120+ views, and zero replies in almost 2 weeks.) Again, the given equations: Energies for Triatomic Model in Cartesian Coordinates: V=\frac{k}{2}(x_{2}-x_{1}-b)^{2}+\frac{k}{2}(x_{3}-x_{2}-b)^{2}...

Hi all - it's been a week, and I still haven't made any progress on this problem. There must be some simple algebra trick I'm missing here. Or maybe my method is completely off? Any thoughts at all?

Let me just add specifically some steps I've taken: R = \frac{\sum m_{i} x_{i}}{\sum m_{i}} = \frac{m(x_{1} + x_{3}) + M x_{2}}{2m + M} = 0 \rightarrow m(x_{1} + x_{3}) + M x_{2} = 0 \rightarrow x_{2} = - \frac{m}{M} (x_{1} + x_{3}) Now using, y_{1} = x_{2} - x_{1} y_{2} = x_{3} - x_{2} I...